局部非线性土与结构相互作用的混合约束模态综合法研究

发布时间：2018-07-06 07:04

本文选题：土 + 结构相互作用　；参考：《天津大学》2015年博士论文

【摘要】：近来年,对土—结构相互作用问题的研究广度和深度逐渐扩大,各类复杂模型越来越庞大且精细化,导致在有限元分析中单元节点的自由度数可谓以十万百万计,需高配置的计算设备和长时间的计算时间才可完成分析,当需多个不同工况的比较时则更成倍地增加工作量,亟待一种可行的既满足计算精度又节省计算成本的分析计算方法。动力子结构法是将土—结构相互作用体系分成若干子系统,先分别求出各子系统的单体反应,然后再联系各单体的反应,使其满足相互作用的条件,从而得到整个体系的反应,大大减少计算量,是一种理想的计算方法,但该方法仅能解决线性问题。本文根据课题组新近提出的能解决局部非线性问题的线性—非线性混合约束模态综合法的思想,在该方法的具体实施方面进行了研究,充分利用现有商业软件的优势,将该方法的实施与ANSYS软件相结合,对实施过程中诸如结构受力全过程中刚度矩阵的提取方法;弹塑性模型中等效弹性模量的计算;一致粘弹性边界问题;以及非线性的接触问题等进行了深入的分析与研究,使混合约束模态综合法能解决复杂状况下的土—结构相互作用体系,开辟了动力子结构法的研究领域。本文主要的创新工作与成果有:1.混合约束模态综合法在ANSYS的实施,首先要解决刚度矩阵提取中的对号入座问题,为此在深入分析ANSYS二次开发四种方法的基础上,决定采取FORTRAN语言的二次开发工具UPFs进行矩阵提取的开发工作,自编程序实现了按照节点编号由小到大的顺序进行矩阵的提取。2.非线性子结构在塑性阶段中的刚度矩阵的提取工作是本文的重点难点之一。为了在非线性时程分析中生成某一时刻的弹塑性刚度矩阵,提出了将非线性塑性区域“等效”为线弹性区域,即在塑性阶段上的小段Δt时间内利用分段等效线性化手段,对结构各个进入塑性阶段的单元进行等效处理,并推导了等效弹性模量的公式,完成了对塑性单元的弹性模量和剪切模量等效工作;利用了ANSYS多点重启动的方法,恢复结构上一时刻的计算结果后能继续进行下一时刻分析;提出了ANSYS与MATLAB程序间的相互调用和控制的操作方法,从而解决了非线性子结构在塑性阶段中的刚度矩阵的有序进行。通过算例模型进行一般性分析,包括Pushover静力非线性分析和简谐波动力时程非线性分析求得响应时程曲线,与ANSYS直接计算法所得到的响应时程曲线比对吻合良好,验证了在弹塑性阶段二次开发的程序文件所提取的矩阵的正确可行。3.建立了考虑局部非线性的地基土—剪力墙结构相互作用的模型,然后根据结构存在局部塑性区域的特点,将整体体系中未进入非线性阶段的区域划分为若干个线性子结构,而将进入塑性阶段的局部区域独立划分为若干个非线性子结构。提出了混合约束模态综合法的详细分析流程并编写了开发程序,着重说明了在ANSYS和MATLAB二者程序之间的实现过程。4.在土—结构相互作用分析模型中,在地基土边界引入一致粘弹性边界条件来模拟半无限域的土体,推导了带有一致粘弹性边界的子结构方程,论证了势能判据截断准则同样适用于带有一致粘弹性边界的线性子结构,证明了采用混合约束模态综合法同样能处理复杂的边界问题。5.通过选择合理的目标面单元和接触面单元、迭代计算接触刚度和设置摩擦系数,将高度非线性的接触问题引入混合约束模态综合法中。提出了箱型基础与周围土体接触关系的处理方法,将接触单元一分为二,目标面单元划入刚度相对较高的箱型基础的线性子结构内,接触面单元划入刚度相对较低的周围土体的非线性子结构内,推导出了箱型基础与周围土体具有接触关系的线性与非线性模态综合方程,拓宽了混合约束模态综合法的应用领域。6.通过算例计算对线性和非线性土体区域给出了推荐范围,当设置一致粘弹性边界时,非线性子结构的区域为2倍的基础宽度,两侧线性子结构区域各为1.5倍的基础宽度,使得模型总体自由度数比使用一般自由边界子结构土体单元自由度数减少很多,从而提高了计算效率。7.进行了混合约束模态综合法扩展到三维土—结构相互作用分析,重点研究了与二维问题的不同之处,重新推导了适合于三维问题的一致粘弹性边界条件的子结构方程;重新推导了箱型基础与周围土体具有接触关系的线性与非线性模态综合方程,以及三维模型等效弹性模量的公式,结果表明混合约束模态综合法能解决三维土—结构相互作用复杂问题。8.在混合约束模态综合法的实施中,通过逐步提取的结构体系全程阶段等效弹塑性刚度矩阵,进行特征值方程计算得到了结构前n阶主要频率和振型在全时段变化情况,从而了解结构刚度在弹塑性动静力分析中的变化规律,可为利用结构动力特性对结构体系进行深入分析研究提供支撑。
[Abstract]:In recent years, the breadth and depth of the soil structure interaction have been expanded and the complex models are becoming more and more large and fine. The free degree of unit nodes in the finite element analysis can be described as one hundred thousand million. It needs high configuration of computing equipment and long time calculation time to complete the analysis, when many different workers are needed. In comparison with the situation, the workload is more multiplied, and a feasible analytical method is needed to satisfy both the calculation precision and the cost of calculation. The dynamic substructure method divides the soil structure interaction system into several subsystems, first to find the single reaction of each subsystem, and then to contact the reaction of the various monomers, so that it satisfies the phase. The condition of interaction, thus obtaining the reaction of the whole system, greatly reducing the amount of calculation, is an ideal calculation method, but this method can only solve the linear problem. In this paper, the idea of the linear nonlinear mixed constraint mode synthesis method which can solve local nonlinear problems recently proposed by the project group is the concrete implementation of this method. In order to make full use of the advantages of the existing commercial software, the implementation of the method is combined with the ANSYS software, and the method of extracting the stiffness matrix in the whole process of structural stress, the calculation of the equivalent elastic modulus in the elastoplastic model, the uniform viscoelastic boundary boundary problem and the nonlinear contact problem are carried out in the implementation process. In the analysis and research, the mixed constrained modal synthesis method can solve the soil structure interaction system under complex conditions and open up the research field of the dynamic substructure method. The main innovation work and achievements of this paper are as follows: 1. the implementation of the hybrid constrained modal synthesis method in the ANSYS, first of all, we should solve the problem of the number of seats in the stiffness matrix extraction. On the basis of the in-depth analysis of the four methods of the two development of ANSYS, the two development tool UPFs of the FORTRAN language is adopted to develop the matrix extraction. The self compiled program realizes the extraction of the stiffness matrix of the.2. nonlinear substructure in the plastic phase according to the node number from small to large. In order to generate the elastoplastic stiffness matrix of a certain moment in the nonlinear time history analysis, it is proposed that the nonlinear plastic region is "equivalent" to the linear elastic region, that is, the piecewise equivalent linearization method is used in the small segment delta T time of the plastic stage, and the units that enter the plastic stage are carried out. The formula of the equivalent elastic modulus is derived, and the equivalent work of the elastic modulus and the shear modulus of the plastic unit is completed. Using the method of ANSYS multi point restart, the next time analysis can be carried out after the recovery of the calculation results at the time of the structure, and the operation of mutual call and control between the ANSYS and the MATLAB program is put forward. This method solves the order of the stiffness matrix of the nonlinear substructure in the plastic stage. Through the example model, the general analysis is carried out, including the Pushover static nonlinear analysis and the harmonic dynamic time history nonlinear analysis to obtain the response time history curve, which is in good agreement with the response time curve comparison obtained by the ANSYS direct calculation method. To verify the correctness and feasibility of the matrix extracted from the program documents developed at the two time of the elastoplastic stage, the model of the soil shear wall structure interaction with local nonlinearity is established by.3.. Then, according to the characteristics of the local plastic region in the structure, the region which has not entered the nonlinear stage in the whole system is divided into several lines. The partial region that enters the plastic stage is divided into several nonlinear substructures independently. The detailed analysis process of the mixed constrained modal synthesis method is proposed and the development program is written. The implementation process between the ANSYS and the MATLAB two programs is emphasized, and the.4. is in the soil structure interaction analysis model, and the foundation is in the foundation. The soil boundary is introduced into the uniform viscoelastic boundary condition to simulate the soil in the semi infinite domain. The substructure equation with the uniform viscoelastic boundary is derived. It is proved that the potential energy criterion truncation criterion is also applicable to the linear substructure with the uniform viscoelastic boundary. It is proved that the mixed constrained modal synthesis method can also deal with complex boundary questions. By selecting the reasonable target surface element and the contact surface element,.5., the contact stiffness and the friction coefficient are iteratively calculated, and the highly nonlinear contact problem is introduced into the mixed constrained modal synthesis method. The contact relationship between the box type foundation and the surrounding soil is proposed. The contact element is divided into two parts and the target surface unit is divided into the stiffness phase. In the linear substructure of the higher box foundation, the contact surface element is inserted into the nonlinear substructure of the surrounding soil with relatively low stiffness. The linear and nonlinear modal synthesis equations of the contact relationship between the box type foundation and the surrounding soil are derived, and the application field of the mixed constrained modal synthesis method,.6., is widened by the calculation example. The range of linear and nonlinear soil is recommended. When the uniform viscoelastic boundary is set, the region of the nonlinear substructure is 2 times the base width and the basic width of the linear substructure of the two sides is 1.5 times, making the total degree of freedom of the model less than the free degree of the soil unit using the general free boundary substructure. The hybrid constrained modal synthesis method is extended to the three-dimensional soil structure interaction analysis, and the difference between the.7. and the two dimensional problem is studied. The substructure equation of the uniform viscoelastic boundary condition suitable for three dimensional problems is rederived, and the contact relation between the box foundation and the surrounding soil is re derived. The linear and nonlinear modal synthesis equations of the system and the formula of the equivalent elastic modulus of the three-dimensional model show that the mixed constrained modal synthesis method can solve the complex problem of the three-dimensional soil structure interaction..8., in the implementation of the mixed constrained modal synthesis method, can be obtained by gradually extracting the equivalent elastoplastic stiffness matrix in the whole process stage of the structure. The eigenvalue equation is used to calculate the changes of the main frequencies and modes of the n order before the structure, so as to understand the change law of the structural stiffness in the elastoplastic dynamic static analysis, which can provide support for the in-depth analysis of the structural system by using the dynamic characteristics of the structure.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TU470

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